Phased arrays, in ultrasonic applications and from the RF to the visible end of the electromagnetic spectrum, provide beam steering with no moving parts. Electronic control replaces mechanical control, which is a tremendous advantage in terms of speed and maintenance. Unfortunately, these advantages are often offset by a cost disadvantage. The number of electronic elements in a circular array is on the order of π(D/λ)2, where D is the diameter of the circular array and λ is the operating wavelength. This comes about as the standard rule is to space antenna elements apart by λ/2 in both directions to suppress sidelobes throughout a hemispherical scan.
In most traditional phased arrays, the control devices are expensive, and in some cases each may require one or more stages of amplification. Even when the active devices are relatively inexpensive, the overall phased array system may require a very deep digital memory to support a large set of focal areas or volumes.
In order to bring the cost down, it is attractive to reduce the number of antenna elements making up the array, thereby reducing the number of control devices, as well as the width of the supporting driver memory.
Simply omitting elements from an originally dense phased array produces a so-called sparse array. Sparse arrays are well known in the ultrasound and microwave/millimeter wave literature to create new problems, particularly the appearance of so called grating sidelobes. That is, in addition to the desired main scanning lobe, there are additional high-level lobes created at different angles. These sidelobes contribute ghosting phenomena to the scanned or imaging process.
Various post-processing remedies have been tried. For example, deconvolution algorithms can be applied, but the most successful of these are nonlinear algorithms which are both scene dependent and very time consuming. Two of the most popular deconvolution algorithms are CLEAN (ref) and Maximal Entropy Method, or MEM (ref). An older, linear (and hence faster and more general) approach is Wiener-Helstrom filtering (ref), but it is well known in that it produces inferior image reconstruction compared to the nonlinear approaches (which are slower and more specialized) such as Maximum Likelihood (ML) iteration (ref) Correlation imaging, involving different subsets of an already sparse array, is also a nonlinear scheme which tends to be quite slow, i.e., not suitable for real-time use. In some cases, such as radioastronomy, one has a priori knowledge of the scene (say, from visible telescopes) which can be used to weed out much of the ghost phenomena. Obviously, this “solution” is inadequate in dealing with a highly dynamic environment.
What is needed is a satisfactory real-time, scene-independent solution to the ghosting problem of reduced element (sparse) arrays.